103 research outputs found
Density-temperature scaling of the fragility in a model glass-former
Dynamical quantities such as the diffusion coefficient and relaxation times
for some glass-formers may depend on density and temperature through a specific
combination, rather than independently, allowing the representation of data
over ranges of density and temperature as a function of a single scaling
variable. Such a scaling, referred to as density - temperature (DT) scaling, is
exact for liquids with inverse power law (IPL) interactions but has also been
found to be approximately valid in many non-IPL liquids. We have analyzed the
consequences of DT scaling on the density dependence of the fragility in a
model glass-former. We find the density dependence of kinetic fragility to be
weak, and show that it can be understood in terms of DT scaling and deviations
of DT scaling at low densities. We also show that the Adam-Gibbs relation
exhibits DT scaling and the scaling exponent computed from the density
dependence of the activation free energy in the Adam-Gibbs relation, is
consistent with the exponent values obtained by other means
Dependence of the fragility of a glass former on the softness of interparticle interactions
We study the influence of the softness of the interparticle interactions on
the fragility of a glass former, by considering three model binary mixture
glass formers. The interaction potential between particles is a modified
Lennard-Jones type potential, with the repulsive part of the potential varying
with an inverse power of the interparticle distance, and the attractive
part varying with an inverse power . We consider the combinations (12,11)
(model I), (12,6) (model II) and (8,5) (model III) for (q,p) such that the
interaction potential becomes softer from model I to III. We evaluate the
kinetic fragilities from the temperature variation of diffusion coefficients
and relaxation times, and a thermodynamic fragility from the temperature
variation of the configuration entropy. We find that the kinetic fragility
increases with increasing softness of the potential, consistent with previous
results for these model systems, but at variance with the thermodynamic
fragility, which decreases with increasing softness of the interactions, as
well as expectations from earlier results. We rationalize our results by
considering the full form of the Adam-Gibbs relation, which requires, in
addition to the temperature dependence of the configuration entropy, knowledge
of the high temperature activation energies ino rder to determine fragility. We
show that consideration of the scaling of the high temperature activation
energy with the liquid density, analyzed in recent studies, provides a partial
rationalization of the observed behavior
The Adam-Gibbs relation for glass-forming liquids in 2, 3 and 4 dimensions
The Adam-Gibbs relation between relaxation times and the configurational
entropy has been tested extensively for glass formers using experimental data
and computer simulation results. Although the form of the relation contains no
dependence on the spatial dimensionality in the original formulation,
subsequent derivations of the Adam-Gibbs relation allow for such a possibility.
We test the Adam-Gibbs relation in 2, 3, and 4 spatial dimensions using
computer simulations of model glass formers. We find that the relation is valid
in 3 and 4 dimensions. But in 2 dimensions, the relation does not hold, and
interestingly, no single alternate relation describes the results for the
different model systems we study.Comment: Submitted to Phys. Rev. Let
Breakdown of the Stokes-Einstein relation in two, three and four dimensions
The breakdown of the Stokes-Einstein (SE) relation between diffusivity and
viscosity at low temperatures is considered to be one of the hallmarks of
glassy dynamics in liquids. Theoretical analyses relate this breakdown with the
presence of heterogeneous dynamics, and by extension, with the fragility of
glass formers. We perform an investigation of the breakdown of the SE relation
in 2, 3 and 4 dimensions, in order to understand these interrelations. Results
from simulations of model glass formers show that the degree of the breakdown
of the SE relation decreases with increasing spatial dimensionality. The
breakdown itself can be rationalized via the difference between the activation
free energies for diffusivity and viscosity (or relaxation times) in the
Adam-Gibbs relation in three and four dimensions. The behavior in two
dimensions also can be understood in terms of a generalized Adam-Gibbs relation
that is observed in previous work. We calculate various measures of
heterogeneity of dynamics and find that the degree of the SE breakdown and
measures of heterogeneity of dynamics are generally well correlated but with
some exceptions. The two dimensional systems we study show deviations from the
pattern of behavior of the three and four dimensional systems both at high and
low temperatures. The fragility of the studied liquids is found to increase
with spatial dimensionality, contrary to the expectation based on the
association of fragility with heterogeneous dynamics
Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test
It has been recognized of late that even amorphous, glass-forming materials
in two dimensions (2D) are significantly affected by Mermin-Wagner type long
wavelength thermal fluctuation which is inconsequential in three (3D) and
higher dimensions. Thus any study of glassy dynamics in 2D should first remove
the effect of such fluctuations. The present work considers the question of
whether the role of spatial dimension on glassy dynamics is only limited to
such fluctuations, or whether the nature of glassy dynamics is intrinsically
different in 2D. We address this issue by studying the relationship between
dynamics and thermodynamics within the framework of the Adam-Gibbs (AG)
relation and its generalization the Random First Order Transition (RFOT)
theory. Using two model glass-forming liquids we find that even after removing
the effect of long wavelength fluctuations, the AG relation breaks down in two
dimensions. Then we consider the effect of anharmonicity of vibrational entropy
- a second factor highlighted recently that can qualitatively change the nature
of dynamics. We explicitly compute the configurational entropy both with and
without the anharmonic correction. We show that the anharmonic correction
reduces the extent of deviation from the AG relation, but even after taking
into account its effects, the AG relation still breaks down in 2D. It is also
more prominent if one considers diffusion coefficient rather than
-relaxation time. Overall, the impact of the anharmonicity of vibration
is larger than the long wavelength fluctuation in determining the qualitative
relation between timescales and entropy. The extent and nature of deviation
from the AG relation crucially depends on the attractive vs. repulsive nature
of the inter-particle interaction. Thus our results suggest that the glassy
dynamics in 2D may be intrinsically different from that in 3D
Glass Transition in Supercooled Liquids with Medium Range Crystalline Order
The origins of rapid dynamical slow down in glass forming liquids in the
growth of static length scales, possibly associated with identifiable
structural ordering, is a much debated issue. Growth of medium range
crystalline order (MRCO) has been observed in various model systems to be
associated with glassy behaviour. Such observations raise the question about
the eventual state reached by a glass former, if allowed to relax for
sufficiently long times. Is a slowly growing crystalline order responsible for
slow dynamics? Are the molecular mechanisms for glass transition in liquids
with and without MRCO the same? If yes, glass formers with MRCO provide a
paradigm for understanding glassy behaviour generically. If not, systems with
MRCO form a new class of glass forming materials whose molecular mechanism for
slow dynamics may be easier to understand in terms of growing crystalline
order, and should be approached in that manner, even while they will not
provide generic insights. In this study we perform extensive molecular dynamics
simulations of a number of glass forming liquids in two dimensions and show
that the static and dynamic properties of glasses with MRCO are different from
other glass forming liquids with no predominant local order. We also resolve an
important issue regarding the so-called Point-to-set method for determining
static length scales, and demonstrate it to be a robust, order agnostic, method
for determining static correlation lengths in glass formers
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